The value of \tan \Bigg(π/4+θ\Bigg)\tan \Bigg(3π/4+θ\Bigg) is

Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET

Best NIMCET Coaching
Aspire Study
Online Classes, Classroom Classes
and More.

Question Id : 11640 | Context :NIMCET 2024

The value of

$\tan \Bigg{(}\frac{\pi}{4}+\theta\Bigg{)}\tan \Bigg{(}\frac{3\pi}{4}+\theta\Bigg{)}$ is

🎥 Video solution / Text Solution of this question is given below:

$\text{Evaluate } \tan\left(\frac{\pi}{4} + \theta\right) \cdot \tan\left(\frac{3\pi}{4} + \theta\right)$

$\tan\left(A + B\right) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$ But we don’t need expansion — use known angle values:

$\tan\left(\frac{\pi}{4} + \theta\right) = \frac{1 + \tan\theta}{1 - \tan\theta}$

$\tan\left(\frac{3\pi}{4} + \theta\right) = \frac{-1 + \tan\theta}{1 + \tan\theta}$

$\left(\frac{1 + \tan\theta}{1 - \tan\theta}\right) \cdot \left(\frac{-1 + \tan\theta}{1 + \tan\theta}\right)$

Simplify:

$= \frac{(1 + \tan\theta)(-1 + \tan\theta)}{(1 - \tan\theta)(1 + \tan\theta)} = \frac{(\tan^2\theta - 1)}{1 - \tan^2\theta} = \boxed{-1}$

$\boxed{-1}$

Get MCA exam-wise questions, solutions, test series & updates instantly on your phone.

🚀 Install Now

Aspire Study Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Aspire Study Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Ask Your Question or Put Your Review.